Work with two small numbers, such as the numbers 2 and 4. Make two lists on a piece of paper. One list shows the number 2 with the exponents of 5, 4, 3, 2, 1 and zero. This is noted as 2^5, 2^4, 2^3, 2^2, 2^1 and 2^0. Make a similar list for the number 4.
Calculate and write down the results for each list. Use a calculator for accurate results. Your first list should show that 2^5 = 32, 2^4 = 16, 2^3 = 8, 2^2 = 4 and 2^1 = 2. Leave 2^0 blank. Calculate and write down the results for the list with the number 4. Leave 4^0 blank.
Examine and study the pattern of the calculations. Start at the top of the list and work down. This will help to determine the results for 2^0 and 4^0.
Notice that the result of 2^5 divided by 2 equals the result for 2^4 (32 divided by 2 = 16). Also note that the result of 2^4 divided by 2 equals the result for 2^3 (16 divided by 2 = 8).
Work your way down the list and notice how each time a result is divided by 2, it equals the next result on the list. This pattern shows that 2^0 = 1. This is the result of 2^1 divided by 2 (2 divided by 2 = 1).
Repeat this process for the list with the number 4. Study the results of the calculations and how they relate to the next result in your list. The pattern shows that each time a result is divided by 4, it equals the next result in the list. By using this pattern, you can see that 4^0 = 1. This is the result of 4^1 divided by 4 (4 divided by 4 = 1).